Italian businessman Cellino has been awaiting approval from the Football League since agreeing a £25million majority stake in the club on February 7.
The delay from the Football League comes as they consider whether Cellino should pass their Owners and Directors Test, formally known as the Fit and Proper Persons Test.
The takeover is in serious doubt, however, after a judge in Sardinia found him guilty of tax evasion on Tuesday.
The Football League has been awaiting full documentation from the court case before reaching a decision on Cellino's deal but it said last Thursday that it would make an announcement within 10 days.
Leeds, however, are pushing for an answer in the next 24 hours after writing to the Football League's in-house lawyer, Nick Craig, on Thursday morning.
A spokesman for current Leeds owners GFH Capital told the Yorkshire Evening Post: "Leeds United have this morning sent a letter to the Football League, demanding that the Football League hands out its decision by the close of play today.
"This is an unprecedented delay which is damaging the owners' ability to move the club forward."
GFH - the investment bank based in Bahrain - has been in control of Leeds since it bought out ex-United chairman Ken Bates in December 2012.